Propagation of sound waves through a linear shear layer: A closed form solution

Closed form solutions are presented for sound propagation from a line source in or near a shear layer. The analysis was exact for all frequencies and was developed assuming a linear velocity profile in the shear layer. This assumption allowed the solution to be expressed in terms of parabolic cyclinder functions. The solution is presented for a line monopole source first embedded in the uniform flow and then in the shear layer. Solutions are also discussed for certain types of dipole and quadrupole sources. Asymptotic expansions of the exact solutions for small and large values of Strouhal number gave expressions which correspond to solutions previously obtained for these limiting cases

Matter Wave Scattering from Ultracold Atoms in an Optical Lattice

We study matter wave scattering from an ultracold, many body atomic system trapped in an optical lattice. We determine the angular cross section that a matter wave probe sees and show that it is strongly affected by the many body phase, superfluid or Mott insulator, of the target lattice. We determine these cross sections analytically in the first Born approximation, and we examine the variation at intermediate points in the phase transition by numerically diagonalizing the Bose Hubbard Hamiltonian for a small lattice. We show that matter wave scattering offers a convenient method for non-destructively probing the quantum many body phase transition of atoms in an optical lattice.Comment: 4 pages, 2 figure

Topology of the polarization field in ferroelectric nanowires from first principles

The behaviour of the cross-sectional polarization field is explored for thin nanowires of barium titanate from first-principles calculations. Topological defects of different winding numbers have been obtained, beyond the known textures in ferroelectric nanostructures. They result from the inward accommodation of the polarization patterns imposed at the surface of the wire by surface and edge effects. Close to a topological defect the polarization field orients out of the basal plane in some cases, maintaining a close to constant magnitude, whereas it virtually vanishes in other cases.Comment: 4 pages, 3 figure

Surface-slip equations for multicomponent nonequilibrium air flow

Equations are presented for the surface-slip (or jump) values of species concentration, pressure, velocity, and temperature in the low-Reynolds number, high-altitude flight regime of a space vehicle. The equations are obtained from closed form solutions of the mass, momentum, and energy flux equations using the Chapman-Enskog velocity distribution function. This function represents a solution of the Boltzmann equation in the Navier-Stokes approximation. The analysis, obtained for nonequilibrium multicomponent air flow, includes the finite-rate surface catalytic recombination and changes in the internal energy during reflection from the surface. Expressions for the various slip quantities were obtained in a form which can be employed in flowfield computations. A consistent set of equations is provided for multicomponent, binary, and single species mixtures. Expression is also provided for the finite-rate, species-concentration boundary condition for a multicomponent mixture in absence of slip

Prediction of the functional properties of ceramic materials from composition using artificial neural networks

We describe the development of artificial neural networks (ANN) for the prediction of the properties of ceramic materials. The ceramics studied here include polycrystalline, inorganic, non-metallic materials and are investigated on the basis of their dielectric and ionic properties. Dielectric materials are of interest in telecommunication applications where they are used in tuning and filtering equipment. Ionic and mixed conductors are the subjects of a concerted effort in the search for new materials that can be incorporated into efficient, clean electrochemical devices of interest in energy production and greenhouse gas reduction applications. Multi-layer perceptron ANNs are trained using the back-propagation algorithm and utilise data obtained from the literature to learn composition-property relationships between the inputs and outputs of the system. The trained networks use compositional information to predict the relative permittivity and oxygen diffusion properties of ceramic materials. The results show that ANNs are able to produce accurate predictions of the properties of these ceramic materials which can be used to develop materials suitable for use in telecommunication and energy production applications